Adaptive content mapping for internet navigation

The Internet as the biggest human library ever assembled keeps on growing. Although all kinds of information carriers (e.g. audio/video/hybrid file formats) are available, text based documents dominate. It is estimated that about 80% of all information worldwide stored electronically exists in (or can be converted into) text form. More and more, all kinds of documents are generated by means of a text processing system and are therefore available electronically. Nowadays, many printed journals are also published online and may even discontinue to appear in print form tomorrow. This development has many convincing advantages: the documents are both available faster (cf. prepress services) and cheaper, they can be searched more easily, the physical storage only needs a fraction of the space previously necessary and the medium will not age. For most people, fast and easy access is the most interesting feature of the new age; computer-aided search for specific documents or Web pages becomes the basic tool for information-oriented work. But this tool has problems. The current keyword based search machines available on the Internet are not really appropriate for such a task; either there are (way) too many documents matching the specified keywords are presented or none at all. The problem lies in the fact that it is often very difficult to choose appropriate terms describing the desired topic in the first place. This contribution discusses the current state-of-the-art techniques in content-based searching (along with common visualization/browsing approaches) and proposes a particular adaptive solution for intuitive Internet document navigation, which not only enables the user to provide full texts instead of manually selected keywords (if available), but also allows him/her to explore the whole database

Commutators of flows and fields

The well known formula [X,Y]=\tfrac12\tfrac{\partial^2}{\partial t^2}|_0 (\Fl^Y_{-t}\o\Fl^X_{-t}\o\Fl^Y_t\o\Fl^X_t) for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms

Nonlinear optics with full three-dimensional illumination

We investigate the nonlinear optical process of third-harmonic generation in the thus far unexplored regime of focusing the pump light from a full solid angle, where the nonlinear process is dominantly driven by a standing dipole-wave. We elucidate the influence of the focal volume and the pump intensity on the number of frequency-tripled photons by varying the solid angle from which the pump light is focused, finding good agreement between the experiments and numerical calculations. As a consequence of focusing the pump light to volumes much smaller than a wavelength cubed the Gouy phase does not limit the yield of frequency-converted photons. This is in stark contrast to the paraxial regime. We believe that our findings are generic to many other nonlinear optical processes when the pump light is focused from a full solid angle.Comment: 6 pages main text + 4 pages appendix, modified abstract and introduction + some other minor change

Spontaneous breaking of rotational symmetry in the presence of defects

We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.Comment: 18 page

Characterisation of the potential of frequency modulation and optical feedback locking for cavity-enhanced absorption spectroscopy

A combination of optical feedback self-locking of a continuous-wave distributed feedback diode laser to a V-shaped high finesse cavity, laser phase modulation at a frequency equal to the free spectral range of the V-cavity and detection of the transmitted laser beam at this high modulation frequency is described for possible application in cavity-enhanced absorption spectroscopy.In order to estimate an absorbance baseline noise of laser intensity and frequency modulated light triplet passed through the V-cavity in open air, a 1.5-cm long optical cell filled by C2H2 at low pressure was placed behind the cavity output mirror. The performance of the setup was evaluated from the experimental bandwidth normalised relative intensity noise on the cavity output and the frequency modulation absorption signals induced by C2H2 absorption in the 1.5-cm cell. From these data we estimate that the noise-equivalent absorption sensitivity of 2.1*10^-11 cm^-1 Hz^-1/2 by a factor of 11.7 above a shot-noise limit can be achieved for C2H2 absorption spectra extracted from the heterodyne beat signals recorded at the transmission maxima intensity peaks of the successive TEM00 resonances.Comment: 18 pages, 8 figures, submitted to Appl. Phys. B 28.07.201

Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks

This paper builds a model which has two extensions over a standard VAR. The …rst of these is stochastic search variable selection, which is an automatic model selection device which allows for coefficients in a possibly over-parameterized VAR to be set to zero. The second allows for an unknown number of structual breaks in the VAR parameters. We investigate the in-sample and forecasting performance of our model in an application involving a commonly-used US macro-economic data set. We …nd that, in-sample, these extensions clearly are warranted. In a recursive forecasting exercise, we …nd moderate improvements over a standard VAR, although most of these improvements are due to the use of stochastic search variable selection rather than the inclusion of breaks

Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers

We transfer the concept of linear feed-back shift registers to quantum circuits. It is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error-correcting codes.Comment: 18 pages, 15 figures, submitted to Proc. R. Soc.

Change-Point Testing and Estimation for Risk Measures in Time Series

We investigate methods of change-point testing and confidence interval construction for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. A key aspect of our work is the ability to detect general multiple structural changes in the tails of time series marginal distributions. Unlike extant approaches for detecting tail structural changes using quantities such as tail index, our approach does not require parametric modeling of the tail and detects more general changes in the tail. Additionally, our methods are based on the recently introduced self-normalization technique for time series, allowing for statistical analysis without the issues of consistent standard error estimation. The theoretical foundation for our methods are functional central limit theorems, which we develop under weak assumptions. An empirical study of S&P 500 returns and US 30-Year Treasury bonds illustrates the practical use of our methods in detecting and quantifying market instability via the tails of financial time series during times of financial crisis